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Volume 26, Issue 2
On Approximation and Computation of Navier-Stokes Flow

Werner Varnhorn & Florian Zanger

DOI: 10.4208/jpde.v26.n2.5

J. Part. Diff. Eq., 26 (2013), pp. 151-171.

Published online: 2013-06

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  • Abstract

We present an approximation method for the non-stationary nonlinear incompressible Navier-Stokes equations in a cylindrical domain (0,T)×G,where G⊂R^3 is a smoothly bounded domain. Ourmethod is applicable to general three-dimensional flow without any symmetry restrictions and relies on existence, uniqueness and representation results from mathematical fluid dynamics. After a suitable time delay in the nonlinear convective term v·∇v we obtain globally (in time) uniquely solvable equations, which - by using semi-implicit time differences - can be transformed into a finite number of Stokes-type boundary value problems. For the latter a boundary element method based on a corresponding hydrodynamical potential theory is carried out. The method is reported in short outlines ranging from approximation theory up to numerical test calculations.

  • Keywords

Navier-Stokes equations regularization time delay finite differences Stokes resolvent hydrodynamical potential theory boundary element methods numerical simulation

  • AMS Subject Headings

35Q30, 76D05, 31B10, 35J25, 45B05, 65N38, 65N40, 76M15, 76M20

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

varnhorn@mathematik.uni-kassel.de (Werner Varnhorn)

fzanger@mathematik.uni-kassel.de (Florian Zanger)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-26-151, author = {Varnhorn , Werner and Zanger , Florian}, title = {On Approximation and Computation of Navier-Stokes Flow}, journal = {Journal of Partial Differential Equations}, year = {2013}, volume = {26}, number = {2}, pages = {151--171}, abstract = {

We present an approximation method for the non-stationary nonlinear incompressible Navier-Stokes equations in a cylindrical domain (0,T)×G,where G⊂R^3 is a smoothly bounded domain. Ourmethod is applicable to general three-dimensional flow without any symmetry restrictions and relies on existence, uniqueness and representation results from mathematical fluid dynamics. After a suitable time delay in the nonlinear convective term v·∇v we obtain globally (in time) uniquely solvable equations, which - by using semi-implicit time differences - can be transformed into a finite number of Stokes-type boundary value problems. For the latter a boundary element method based on a corresponding hydrodynamical potential theory is carried out. The method is reported in short outlines ranging from approximation theory up to numerical test calculations.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v26.n2.5}, url = {http://global-sci.org/intro/article_detail/jpde/5159.html} }
TY - JOUR T1 - On Approximation and Computation of Navier-Stokes Flow AU - Varnhorn , Werner AU - Zanger , Florian JO - Journal of Partial Differential Equations VL - 2 SP - 151 EP - 171 PY - 2013 DA - 2013/06 SN - 26 DO - http://doi.org/10.4208/jpde.v26.n2.5 UR - https://global-sci.org/intro/article_detail/jpde/5159.html KW - Navier-Stokes equations KW - regularization KW - time delay KW - finite differences KW - Stokes resolvent KW - hydrodynamical potential theory KW - boundary element methods KW - numerical simulation AB -

We present an approximation method for the non-stationary nonlinear incompressible Navier-Stokes equations in a cylindrical domain (0,T)×G,where G⊂R^3 is a smoothly bounded domain. Ourmethod is applicable to general three-dimensional flow without any symmetry restrictions and relies on existence, uniqueness and representation results from mathematical fluid dynamics. After a suitable time delay in the nonlinear convective term v·∇v we obtain globally (in time) uniquely solvable equations, which - by using semi-implicit time differences - can be transformed into a finite number of Stokes-type boundary value problems. For the latter a boundary element method based on a corresponding hydrodynamical potential theory is carried out. The method is reported in short outlines ranging from approximation theory up to numerical test calculations.

Varnhorn , Werner and Zanger , Florian. (2013). On Approximation and Computation of Navier-Stokes Flow. Journal of Partial Differential Equations. 26 (2). 151-171. doi:10.4208/jpde.v26.n2.5
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